Prof Bernhard Von Stengel COL 4.12

This course is available on the BSc in Business Mathematics and Statistics, BSc in Management, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business, BSc in Psychological and Behavioural Science and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

The course emphasises a formal treatment of mathematical Game Theory through definitions, theorems and proofs. Familiarity with a rigorous treatment of mathematics is expected. Basic knowledge of matrices as covered in Mathematical Methods (MA100) or Quantitative Methods (MA107) as well as some knowledge of probability is required.

Concepts and methods of mathematical game theory with some applications to economics. Nim and combinatorial games. Congestion games. Game trees with perfect information. Backward induction. Extensive and strategic (normal) form of a game. Expected utility. Nash equilibrium. Commitment. Zero sum games, mixed strategies, maxmin strategies. Nash equilibria in mixed strategies. Finding mixed-strategy equilibria for two-person games. Extensive games with information sets, behaviour strategies, perfect recall. If time permits: The Nash bargaining solution, multistage bargaining, private-value auctions.

20 hours of lectures and 10 hours of classes in the MT. 2 hours of lectures in the ST.

Written answers to set problems will be expected on a weekly basis.

Lecture notes will be provided. Further reading: K Binmore, Playing for Real: Game Theory, CUP, 2007; E Mendelson, Introducing Game Theory and Its Applications, CRC 2004.

Exam (100%, duration: 2 hours) in the summer exam period.